Adaptive structures, systems incorporating same and related methods

ABSTRACT

Adaptive structures, systems incorporating such adaptive structures and related methods are disclosed. In one embodiment, an adaptive structure is provided that includes a first structure and at least one microstructure associated with the first structure. The at least one microstructure may include a microscale beam configured to be displaced relative to the first structure upon the adaptive structure being exposed to a specified temperature. The beam may be formed for example, of a metallic material, of multiple different metallic materials, or of a shape memory alloy. In one embodiment, a plurality of the adaptive structures may be associated with micropores of a skin panel. The adaptive structures may be utilized to control the flow rate of a coolant or other fluid through the micropores responsive to a sensed environmental parameter such as, for example, temperature.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. patent application Ser. No.11/556,988, filed Nov. 6, 2006, which issues as U.S. Pat. No. 7,913,928on Mar. 29, 2011, which claims the priority filing date of United StatesProvisional Patent Application Serial No. 60/733,980 filed Nov. 4, 2005,the disclosure of each of which is hereby incorporated by referenceherein in its entirety.

FIELD OF THE INVENTION

The present invention is related generally to adaptive structures,systems incorporating such adaptive structures and related methods. Moreparticularly, the present invention is related to mechanisms andstructures constructed and operative at the microscale that may be usedindividually or as part of a system for adapting and responding toenvironmental changes including time varying and location varyingenvironmental parameters.

BACKGROUND OF THE INVENTION

There are numerous circumstances in which a structure experiences timevaried and location varied state changes. Such state changes may beheavily influenced by the environment in which the structure is placedor is operating. For example, there are numerous structures thatexperience a change in temperature, with the temperature varying fromone location of the structure to another (i.e., temperature gradientsand localized heating or cooling of the structure), and wherein thestructure experiences changes in temperature at different times. Inother words, such a temperature or other condition is often transientand asymmetric in multiple dimensions.

Often, it is desirable to manage the temperature (or other parameter orcondition) of such structures. However, efforts to control suchparameters in a structure have conventionally included “blanket”approaches that are generally conservatively designed, often forworst-case scenarios.

For example, one structure that is desirably maintained within a certaintemperature range includes the leading edge of a wing foil on supersonicor hypersonic aerospace vehicle. Similarly, the wall (or some othercomponent) of an engine that is associated with high-speed aerospacevehicles experiences substantial temperature variations and may requiresome form of thermal management for effective operation of the vehicle.Depending, for example, on the current speed of the vehicle, theacceleration pattern of the vehicle and numerous other parameters, suchsurfaces and structures may experience very substantial temperatureincreases, with such increases sometimes occurring at a rather rapidpace and in a non-uniform manner.

Conventional cooling approaches for structures associated with, forexample, high-speed aerospace vehicles, can be broadly classified asfilm cooling, where the wall is covered with a thin film of freshcoolant (often fuel), transpiration cooling, where the coolant issupplied uniformly through a porous wall, and wall cooling, wherecoolant flow convectively cools the back side of the wall.Conventionally, these approaches are implemented passively wherein oneor more arrays of fixed orifices are supplied with a pressurized coolantwithout substantial control over the volume of coolant or the locationto which such coolant is supplied. Such approaches can often present anumber of challenges and problems.

During the trajectory of a typical hypersonic air-breathing vehicle(e.g., Mach 2-15), the heat transfer thermal loads can varydramatically, from take-off to the mission altitude, as illustrated inFIG. 1. FIG. 1, which illustrates the large temporal variations of heatload on the external skin of a hypersonic vehicle for a typical mission,shows that the maximum convective heat transfer coefficient, “h” and theadiabatic wall temperature, T_(aw) occur at different times in thetrajectory of such a vehicle (note that the speed of such a vehicleafter 95 seconds is approximately Mach 3). Such large variations inthermal loads impose tremendous demands on a vehicle thermal managementsystem, typically requiring the cooling system to be designed for afixed worst-case trajectory point. Though this design approach mayprovide adequate cooling at the highest thermal loads point, it comes atthe expense of potentially over-cooling at other “off-design” points.This approach is inefficient, requires an undesirably high volume ofcoolant and places stringent demands on the thermal management systemfor the entire mission.

Similar inefficiencies may result from the spatial distribution ofthermal loads over the surface of the structure being cooled.Uncertainty in predicting the temperature at any particular locationwithin a given structure (e.g., the inlet, combustor, or nozzle walls ofan engine) will lead to conservative coolant flow rates for the entirestructure.

Numerous other structures likewise function more effectively ifmaintained within a desired temperature range (or within other specifiedparameter limits) but suffer from similar inefficiencies in maintainingthe desired parameters. For example, with respect to temperature orthermal management, other examples of structures, where it is desirableto maintain the structure within a specified temperature range includesgas turbine blades, nuclear reactors, combustors, heat exchangers,rocket engines and various components of aerospace vehicles includinghypersonic vehicles. In actuality, the number of components andstructures that require some kind of parameter (e.g., thermal)management, and wherein the parameter is transient and asymmetrical isvirtually limitless.

It is an ongoing desire to improve management of other parameters thatmay be time or spatially varied (or both). It would be advantageous toimprove the efficiency and effectiveness of such parameter managementincluding the use of structures, systems and methods that are adaptivein nature. For example, it is an ongoing desire to improve thermalmanagement of various structures that exhibit time varied or spatiallyvaried temperature changes.

SUMMARY OF THE INVENTION

In accordance with various embodiments of the present invention,adaptive structures, systems incorporating such adaptive structures andrelated methods are provided. In accordance with one embodiment of thepresent invention, a thermal management system is provided. The systemincludes a skin panel having a first surface, a second surface and atleast one micropore extending from the first surface and the secondsurface. A flow path extends between a source of coolant and the atleast one micropore. At least one adaptive structure is associated withthe at least one micropore and is configured to alter a flow rate ofcoolant through the at least one micropore responsive to temperaturesensed by the at least one adaptive structure.

In accordance with another embodiment of the present invention, anadaptive structure is provided. The adaptive structure includes a firststructure and at least one microstructure associated with the firststructure. The at least one microstructure includes a microscale beamconfigured to be displaced relative to the first structure upon theadaptive structure being exposed to a specified temperature.

In accordance with yet another embodiment of the present invention, amethod of cooling a structure is provided. The method includes providinga source of coolant and flowing coolant from the source to a skin panelassociated with the structure and through at least one micropore formedin the skin panel. An adaptive structure is associated with the at leastone micropore and a temperature is sensed by the adaptive structure. Aflow of coolant through the at least one micropore is altered by theadaptive structure responsive to the sensed temperature.

DESCRIPTION OF THE DRAWINGS

The foregoing and other advantages of the invention will become apparentupon reading the following detailed description and upon reference tothe drawings in which:

FIG. 1 is a graph related to heating issues and thermal management of anaerospace vehicle.

FIG. 2A shows an aerospace vehicle in accordance with an embodiment ofthe present invention;

FIGS. 2B-2D show progressively enlarged, partial cross-sections of acomponent or structure of the aerospace vehicle of FIG. 2A;

FIG. 2E shows a cross-sectional view of a microstructure utilized inconjunction with the structure set forth in FIGS. 2B-2D;

FIG. 2F shows a perspective view of another microstructure in accordancewith another embodiment of the present invention;

FIG. 2G shows a plan view of yet another microstructure in accordancewith a further embodiment of the present invention;

FIG. 2H shows an enlarged cross-sectional view of another portion of thestructure shown in FIG. 2B including yet another microstructure inaccordance with another embodiment of the present invention;

FIGS. 3A and 3B show a perspective view and a side view, respectively,of a clamped-clamped beam with an eccentricity;

FIGS. 4A and 4B show side views of a pinned-pinned simplification of aclamped-clamped buckling problem, showing pinned deflection v(x) in FIG.4A and clamped deflection d(x) in FIG. 4B;

FIGS. 5A and 5B illustrate equivalent loadings of pinned-pinned beams;

FIG. 6 shows nondimensional design curves for deflection, δ=d/h, as afunction of temperature rise, θ=12 αΔT(L/πh)², for variouseccentricities, ε=e/h;

FIG. 7 shows nondimensional design curves for stress, Σ=(σ_(M)/E)(L/h)²,as a function of temperature rise, θ=12αΔT(L/πh)², for variouseccentricities, ε=e/h;

FIG. 8 shows nondimensional stress components for a beam;

FIG. 9 shows inflection point location (θ*, δ*) as a function offabricated beam eccentricity, ε;

FIGS. 10A and 10B are schematics of an experimental setup;

FIGS. 11A and 11B show central deflection versus temperature riseresults for the various beam geometries plotted against the theoreticalpredictions for (a) e/h=0.05 and (b) e/h=0.0125;

FIGS. 12A and 12B show nondimensional central deflection, 6, versusnondimensional temperature rise, θ, results for the various beamgeometries plotted against the theoretical predictions for (a) ε=0.05and (b) ε=0,0125; and

FIGS. 13A and 13B show repeatability of test results.

DETAILED DESCRIPTION OF THE INVENTION

Referring to FIG. 2A, an aerospace vehicle 100 is shown that has one ormore components, structures or surfaces that experience transientparameter changes, asymmetrical parameter changes, or both, duringoperation thereof. For example, an engine wall 102, a nozzle wall orsome other component associated with a propulsion system may experiencevarying temperatures during operation of the vehicle 100. Othercomponents, such as a leading edge of an air foil 104 (or various othersurfaces) may likewise experience transient and asymmetrical temperaturechanges. As shown in FIG. 2B, considering the wall 102 of an engine asan example, air flow 106 passes through a passage of the engine (such asa nozzle) at a rapid flow rate. In aerospace vehicles 100 that aredesigned, for example, to travel at a very high rate of speed, such asair breathing hypersonic vehicles (vehicles that travel at a rate ofspeed between approximately Mach 2 and Mach 15), temperatures within theengine may reach extreme levels and, therefore, require a thermalmanagement system to transfer heat away from the engine wall 102 (orother structure) as generally indicated at 108.

As shown in FIG. 2C, a thermal management system in accordance with oneembodiment of the present invention may include a source of coolant 110that passes along a flow path 112 to be distributed along a portion ofthe engine wall 102. The coolant 110 may be supplied as a pressurizedcoolant and, in one embodiment, may include fuel from the vehicle 100.As shown in FIGS. 2C and 2D, a structure, referred to herein as a skinor a skin panel 114, is associated with the engine wall 102 and mayinclude one or more micron sized pores 116 through which the coolant 110may flow, as needed or desired, for cooling the engine wall 102. In oneembodiment, the skin panel 114 may be formed the exhibit a thickness ofapproximately 1 millimeter (mm) while the pores 116 may exhibit adiameter or cross-sectional width of approximately 100 to 200micrometers (μm).

In accordance with an embodiment of the present invention, an adaptivestructure may be associated with a pore 116 and utilized to control theflow of the coolant 110 therethrough. For example, as shown in FIG. 2E,the adaptive structure 118 may be used to limit the flow of coolant 110through an associated pore 116 in an adaptive manner responsive to, forexample a temperature sensed by the adaptive structure 118. Thus,adaptive structure 118 may be said to “sense” the surroundingtemperature, even in the absence of a dedicated sensor element. In oneembodiment, the adaptive structure 118 may include an actuator ormicrostructure (a structure formed at the microscale). The actuator mayinclude a flap or a beam 120 formed of a desired material and exhibitinga desired shape such that, in reaction to an increase in temperature,and as indicated by a dashed line, the beam 120 deflects away from theopening 122 of its associated pore 116 (e.g., due to thermal expansionof the beam 120 or a portion thereof), enabling the flow rate of coolant110 through the pore 116 to increase. Upon a decrease in temperature,the beam 120 may deflect back toward the opening 122 of the pore 116,again changing the flow rate of coolant through the pore 116.

The beam 120 may be configured to deflect, or be displaced, upon sensingof one or more threshold temperatures to provide a flow rate of coolant110 that is adequate to transfer a desired amount of heat away from thestructure (e.g., the engine wall 102) and maintain the structure withina specified temperature range. Moreover, not only may the beam 120 beconfigured to be actuated at a desired temperature (or within a desiredtemperature range), but the beam 120 may also be configured to bedisplaced in accordance with a desired relationship with the temperaturevariation of the structure (e.g., the engine wall 102). For example, thebeam 120 may be configured to exhibit a linear or a nonlineardisplacement relationship with the temperature variation of theassociated structure depending on specific cooling needs. Such tailoringof the flap or the beam 120 may be accomplished, for example, bytailoring the geometric configuration of the flap or the beam 120, bytailoring the material from which the flap or the beam 120 is formed,through the manner in which the flap or the beam 120 is coupled to anunderlying material, or a combination of such techniques.

A plurality of such adaptive structures 118 formed in association withthe skin panel 114 provides a self-regulating thermal management systemand results in more efficient thermal management of a structure thatexhibits, for example, a highly transient thermal profile. Such athermal management system generally behaves similar to the human skin,and more particularly to the sweat gland, when it responds to a thermalstimulus by providing a tailored amount of cooling in a localized areabased on need. In the case of the adaptive structure 118 or otherembodiments of the present invention, the flow of coolant isautomatically adjusted in response to an external flow-field heat flux.

Thus, a structure needing thermal management may have one or moresurfaces covered with large arrays of adaptive structures 118 or otherself-regulating coolant pores that control the flow rate of coolant forfilm, transpiration, or wall cooling. Each pore 116, or sub-array ofpores 116, may independently control the flow rate of coolant 110passing therethrough such that coolant flow rates vary with the thermalload to maintain the temperature of the structure within a desiredoperational range. Moreover, such adaptive structures 118, because theyare formed at the micron scale, introduce very minimal flow disturbancewhile saving considerable weight and providing fast response times ascompared to conventional thermal management systems.

Referring briefly back to FIG. 1, if a conventional thermal managementsystem were designed for the highest heat flux expected throughout ahypersonic vehicle mission (e.g., at approximately 6 seconds in FIG. 1),it is believed that the resulting total heat load integrated over the 95second mission would be overestimated by approximately 74%. A thermalmanagement system configured with adaptive structures in accordance withone or more embodiments of the present invention would enable anaerospace vehicle to significantly reduce the amount of fuel requiredfor cooling due to the use of coolant as needed, rather than based onconservative design parameters.

Referring back to FIGS. 2A-2E, the self-regulating skin panel 114,including the adaptive structures 118, may be fabricated usingmicrofabrication processes utilized in the semiconductor andmicroeletromechanical systems (MEMS) industries as will be appreciatedby those of ordinary skill in the art. Such processes may include, forexample, film deposition, lithographic patterning, and etching to createplanar arrays of devices or adaptive structures having micron (ormicrometer) scale features on or through, for example, a Si or SiCsubstrate. The skin panels 114 may be mounted to coolant distributionwebs, which may be integrally formed with the structure that is beingcooled (e.g., the engine wall 102) such as, for example, through fusionbonding, brazing, or glass bead fusing.

As will be appreciated by those of ordinary skill in the art, MEMStechnology allows the integration of a sensor, an actuator, andelectronics on an area smaller than the size of a pupil. The use of MEMSor semiconductor fabrication processes to provide adaptive structures inaccordance various embodiments of the present invention provides variousadvantages. For example, batch fabrication at large volumesconventionally results in cost reduction. Additionally, as previouslynoted, the small structure or device size that is produced providesweight savings, localized response, minimal flow disturbance and rapidresponse. Moreover, the use of such structures or devices providessignificant redundancy since thousands of MEMS or MEMS-like structurescan be fabricated on a single chip having a surface area of only 1 mm×1mm. Additionally, such structures and devices consume very little power.Indeed, in certain embodiments, wherein the material properties of thebeam 120 of the adaptive structure 118, no power is consumed byoperation of such structures or devices. Various other advantages areoffered by use of microscaled structures and devices as will be apparentto those of ordinary skill in the art.

Referring briefly to FIG. 2F, a perspective view of another adaptivestructure 118′ is shown. The adaptive structure 118′ includes anactuator in the form of an elongated slender beam 120′ that, rather thanbeing free at one end (or cantilevered at a single end thereof), isconstrained at both ends, causing the beam to buckle in the middle uponactuation thereof Thus, when in a nonactuated state, such as when thetemperature of an associated structure is below a threshold temperature,the actuator or beam 120′ remains in an unactuated state (as shown indashed lines) to prevent, or at least limit, the flow of coolant 110through an associated pore (not shown in FIG. 2F). When actuated, theactuator or beam 120′ buckles such that the central portion thereofdeflects away from the skin panel 114 to increase the flow rate ofcoolant through the pore. It is additionally noted that, in theembodiment shown in FIG. 2F, the actuator or beam 120′ is not located onthe surface of the skin panel 114 that is exposed to the heat source,but is located on an opposing side thereof

Referring now to FIG. 2G, a plan view is shown of another adaptivestructure 118″ that is formed at the microscale. The adaptive structure118″ includes beam having a main body portion 130 sized and configuredto cover, or at least substantially cover, the opening 122 of anassociated pore 116. One or more lateral displacement members 132 arecoupled with the main body portion 130 and attached to, or otherwiseintegrated with, the skin panel 114. The displacement members 132 may beappendages from the main body portion 130 and substantially integrallyformed therewith, or they may be coupled to the main body portion 130 bysome other means.

When the structure (e.g., engine wall 102 (FIG. 2A)) to which theadaptive structure is attached exhibits a temperature below a thresholdlevel, the displacement members 132 remain in a first, nonactuatedposition (shown in dashed lines) such that the main body portion covers,or at least partially covers, the opening 122 of the pore 116 to preventor limit flow of coolant 110 therefrom. Upon reaching or exceeding athreshold temperature, the displacement members 132 deflect laterallyrelative to the pore 116 to expose a larger area of the opening 122 andincrease the flow rate of the coolant 110. It is noted that the adaptivestructure 118″ deflects laterally (i.e., in a direction that isgenerally parallel with respect to a surface of skin panel 114 withwhich the adaptive structure 118″ is associated). This is in contrast tothe embodiment previously described wherein the beam 120 is displacedaway from or toward the surface of the skin panel 114.

Referring now to FIG. 2H, an enlarged portion of air foil 104 is shownwhich incorporates an adaptive structure 140 in accordance with yetanother embodiment of the present invention. While the previouslydescribed embodiments included adaptive structures that could, ifdesired, be exposed to a flow path (such as an air flow path within aportion of an engine), it may be desirable at times to provide coolingin a manner such that the coolant does not enter into such a flow pathand such that the adaptive structure is likewise not exposed to such aflow path. One example of such a cooling technique includes impingementcooling or wall cooling wherein coolant is sprayed against (or otherwisecontacts) a backside or a surface of the structure that is relativelyremote from the source of heat to which the structure is exposed.

For example, the leading edge of structure such as an air foil 104 tendsto experience significant temperature increases in high-speed aerospacevehicles. In some instances, it may be desirable to cool the air foil104, or portions thereof, without exposing the adaptive structure 140 orother components to the air stream 142, which is passing over the airfoil 104. Thus, a thermocouple 144 or other device may be embedded in orotherwise be associated with a portion of the air foil 104 to sense achange in temperature experienced by the air foil 104 at a particularlocation. Due to the thermoelectric effect employed by the thermocouple(generally the effect of converting a temperature differential to anelectrical voltage and vice versa, as will be appreciated by those ofordinary skill in the art), an electrical voltage may be established viaan electrical conductor 146 to actuate a beam 148 or other displaceablecomponent of the adaptive structure 140.

The beam 148 may be disposed within a coolant flow path 150 such that,prior to actuation (such as shown by dashed lines) the beam 148 or aportion thereof prevents, or at least limits, the flow of coolant 110that is to impinge upon the back surface 152 of the air foil 104 orother structure. Upon application of the voltage from the thermocouple144, the beam 148 is displaced (such as indicated by solid lines) suchthat the flow rate of coolant 110 is increased.

In one embodiment, the displaceable component or beam 148 may be formedfrom a shape memory alloy (SMA). In one particular embodiment, thedisplaceable component or beam 148 may be formed of an SMA materialincluding nickel and titanium. One more specific example includes amaterial commercially known as Nitinol, which includes approximately 55%nickel by weight and approximately 45% titanium by weight. As discussedin further detail below, the SMA is a material that is deformed andthen, when heated, returns to its original form or shape.

It is noted that, because various components of the adaptive structure140 are not exposed to, for example, the flow path of the air stream 142or some other harsh environment, that a wider range of materials may beconsidered for use in providing and operating the adaptive structure140.

Functionally, the adaptive structure 140 can be viewed as a combinationof a sensor, an actuator, and a control subsystem. Using MEMStechnology, these functions may be integrated on a chip to provideautonomous, local thermal management. As already mentioned, numerousapproaches are possible to implement such a device or adaptive structurefor sensing, actuation, and control.

For film and transpiration cooling, the adaptive structure may often beexposed to harsh environments and, therefore, traditional electroniccircuitry may not be desirable or feasible if the adaptive structurewere to be directly collocated with the sensor and actuator device.Instead, a thermomechanical control approach may be used (i.e., withoutelectronics) such as has been described with particular reference toFIGS. 2E and 2F. For example, a local increase in wall temperature willlead to a mechanical deformation (via thermal expansion), which in turnaffects the coolant flow rate. Not using analog or digital electronicsmay limit the control algorithms to the simplest strategies, such asproportional control. However, the thermomechanical implementation canbe extremely simple, reliable, completely autonomous, require noexternal wiring, and be suitable for use in high temperatureenvironments.

Multiple sensing and actuation approaches are contemplated inconjunction with embodiments of the present invention. For example, asalready described, differential thermal expansion may be used as amechanical actuation and control mechanism. In such a case, thermalexpansion, due to temperature gradients, results in non-uniformexpansion of the adaptive structure (or actuating component thereof).Such a mechanism may be implemented using SiC and used in hightemperature environments. Additionally, such an approach enables theadaptive structure to exhibit a substantially linear response. It isnoted, however, the differential expansion conventionally results inrather small deflections and such a mechanism is rather sensitive totemperature distributions.

Bimorph thermal expansion is similar to differential thermal expansion,but utilizes multiple materials having different thermal expansioncoefficients so as to induce non-uniform deformation. Deflections of alarger magnitude, as compared to differential expansion, are possibleusing bimorph expansion and such a mechanism is less sensitive totemperature distribution. However, response of bimorph structures ismoderately nonlinear and construction of a structure based on bimorphexpansion is more involved because it inherently requires the use of twohigh temperature materials (e.g., two different metallic materials).

Shape memory alloys, briefly discussed hereinabove, are unique materialsthat undergo a material property phase transformation in their crystalstructure that is temperature dependent. This phase transformation isresponsible for the shape memory and superelastic properties of thesealloys. These metallic materials possess the ability to return to somepreviously defined shape or size when subjected to certain temperaturecharacteristics. SMAs can be plastically deformed at some relatively lowtemperature and can then be returned to their original shape onceexposed to some higher temperature. When the SMA is heated above itstransformation temperature, it can recover a preset shape and size; uponcooling, the SMA returns to an alternate shape.

Considering the above example of NiTi, the transformation temperaturefor NiTi (or Nitinol) ranges from 30° F. to 250° F. and can occur eitherby direct heat or by applying an electric current that generates heat(ohmic heating). Thin film NiTi can also be superelastic and, in acertain state, behaves like rubber in that it is capable of attainingextreme angles and may be deformed into small shapes. In its oppositestate, the NiTi material resorts to a different shape and is very rigid.NiTi is very flexible and possesses the largest energy density of anyactive material, generating a large force during the shape changingprocess.

Relatively large deflections are possible using SMAs (as compared to thedifferential expansion and the bimorph expansion mechanisms) andtemperature distribution is less critical. However, operatingtemperatures may be limited when using SMAs and, furthermore, structuresformed of SMAs tend to exhibit a highly nonlinear response.

With regard to sensing approaches, examples include direct thermalsensing, conductive thermal sensing and thermoelectric approaches.Direct thermal sensing includes exposing the adaptive structure, or atleast the actuator component thereof, directly to the heat source (e.g.,hot gases). Such an approach provides relative certainty in the resultsof the sensing. However, direct sensing, depending on the environment inwhich the sensor is exposed, may require the use of high temperaturematerials in the adaptive structure. The terms “sense, “sensing” andvariants thereof are used herein in a nonlimiting manner, to indicatethe passive or active recognition by an element or feature or acombination of elements or features of an adaptive structure, of one ormore stimuli in the form of variations in selected parameters such as,for example, temperature, such recognition being usable to initiate orvary a response by the adaptive structure.

Conductive thermal sensing includes sensing heat that is conducted froma surface of the structure being cooled to the actuator or sensor of theadaptive structure. While there is relatively less certainty in sensingthe actual temperature, such an approach enables the adaptive structureto operate at a relatively lower temperature.

Thermoelectric sensing includes sensing the temperature of a structure,for example, at or near a surface that is exposed to the heat sourceusing a thermocouple or similar device to establish an electricpotential. Such an approach enables the sensing to take place relativelyremotely from the actuating component (e.g., the displaceable member) ofthe adaptive structure, but it may also limit operating temperatures tosome degree.

While the various embodiments described herein have generally beendiscussed in the context of providing a thermal management system for ahigh-speed aerospace vehicle, it is noted that the present invention,including the various embodiments of adaptive structures, may beutilized in a number of different contexts and applications.

Embodiments of the present invention may be used in numerous otherthermal management applications including, for example, gas turbinecooling, nuclear reactors, combustors, heat exchangers, rocket engines,or even cooling of electronic components such as microchips.

Embodiments of the present invention may also be used for inapplications other than thermal management systems. For example, varioustypes of flow controls may be managed by embodiments of the presentinvention. One example includes control of impulse thrust of, forexample, a missile or rocket, enabling directional thrust to be effectedthrough a desired surface of the missile or rocket and providing therocket or missile with a high degree of maneuverability.

Other embodiments of the present invention may include positioningadaptive structures having, for example, flaps as an actuating device onan air foil. At certain times during flight, it may become desirable toperturb the boundary layer about the air foil. Such adaptive structuresmay be used to effect such a perturbation.

In yet another embodiment, such adaptive microstructures may be utilizedin sensing flow separation about an air foil and responding to such flowseparation in a desired manner.

EXAMPLE

Considering a long slender beam as an actuation device in an adaptivestructure, a long slender beam in compression will exhibit a lateraldeflection as the loading approaches a critical value and the beambecomes unstable. A beam with a perfectly symmetric cross section willbuckle in a discontinuous manner at the critical load. A perfectlysymmetric cross section, however, is a theoretical approximation. Inreality, a compressive member will have some imperfection or asymmetrythat leads to a continuous nonlinear deflection. Accordingly, thebuckling of compressed beams with a designed eccentricity has beeninvestigated, focusing on the regime of small eccentricity ratios, e/h→0(e being the eccentricity or offset and h being the thickness of thebeam), for the specific geometry shown in FIGS. 3A and 3B.

The Elastic Curve and the Secant Formulation

An elastic analysis of clamped-clamped beams under thermal loading wascarried out with the assumption of small curvatures. Due to symmetry, aclamped-clamped beam of length 2L buckling under a compressive force canbe analyzed as a pinned-pinned beam of length L under the same loading.

The pinned ends correspond to inflection points in the clamped beam,where the internal moment is null. The resulting deflections can beextended accordingly to the clamped-clamped case as shown in FIGS. 4Aand 4B.

The clamped eccentric beam in FIGS. 3A and 3B can also be simplified asa pinned beam; in this case, the inflection points of the beam coincidewith the eccentricity locations. More specifically, the point of zeromoment in the beams is located at half the eccentric height, e/2. Theresultant loading and deflection of the beam is, therefore, symmetricabout this point. Using this simplification, the elastic curve and thestate of stress have been analyzed.

The pinned beam-column with a compressive load, P, applied at aneccentric distance, e/2, is statically equivalent to an axially loadedbeam with an additional moment, M₀=Pe/2, applied at the end points asshown in FIGS. 5A and 5B.

Assuming shallow beam curvatures but considering the moment induced bylateral deflection of the beam, the elastic curve for the beam is givenas:

where v is the pinned-pinned deflection, I is the beam moment of inertiaand E is the modulus of elasticity. The resultant problem becomes:

$\begin{matrix}{{{\frac{^{2}v}{x^{2}} + {\left( \frac{P}{EI} \right)v}} = {- \frac{Pe}{2\; {EI}}}}{{{v(0)} = {{v(L)} = 0}},}} & (2)\end{matrix}$

which has the following solution:

$\begin{matrix}{{v(x)} = {{\frac{e}{2}\left\lbrack {{{\tan \left( {\frac{L}{2}\sqrt{\frac{P}{EI}}} \right)}{\sin \left( {\sqrt{\frac{P}{EI}}x} \right)}} + {\cos \left( {\sqrt{\frac{P}{EI}}x} \right)} - 1} \right\rbrack}.}} & (3)\end{matrix}$

As seen in FIGS. 4A and 4B, the central deflection of the associatedclamped-clamped problem, d, is twice that of the central deflection ofthe pinned-pinned problem, v(x=L/2), hence:

$\begin{matrix}{d = {{2\; {v\left( {x = {L/2}} \right)}} = {{e\left\lbrack {{\sec\left( {\frac{L}{2}\sqrt{\frac{P}{EI}}} \right)} - 1} \right\rbrack}.}}} & (4)\end{matrix}$

Maximum Stress

A buckled beam under compressive loading is subjected to both axial andbending stress, the maximum of which is compressive and located at themidpoint on the lower surface of the beam, as drawn in FIGS. 4A and 4B.The maximum stress can be written as the sum of these two components:

$\begin{matrix}{\sigma_{M} = {{\sigma_{A} + \sigma_{B}} = {\frac{P}{bh} + {\frac{h}{2\; I}{{{M\left( {x = {L/2}} \right)}}.}}}}} & (5)\end{matrix}$

Using the magnitude of the internal moment at the midpoint, as given byEq. (1):

$\begin{matrix}{{{{M\left( {x = {L/2}} \right)}} = {{P\left( {\frac{e}{2} + {v\left( {x = {L/2}} \right)}} \right)} = {\left( \frac{Pe}{2} \right){\sec \left( {\frac{L}{2}\sqrt{P/{EI}}} \right)}}}},} & (6)\end{matrix}$

yields the maximum stress in the buckled beam:

$\begin{matrix}{\sigma_{M} = {{\frac{P}{bh}\left\lbrack {1 + {3\left( {e/h} \right){\sec \left( {\frac{L}{2}\sqrt{P/{EI}}} \right)}}} \right\rbrack}.}} & (7)\end{matrix}$

Equations (4) and (7) define the beam central deflection and maximumstress as a function of axial load. An additional relation is needed torelate the axial force, P, to the average beam temperature rise, ΔT.

Stress-Strain-Temperature Relationship

Consider the stress-strain relationship of a heated beam restrained fromexpansion in the axial direction:

$\begin{matrix}{\sigma_{A} = {\frac{P}{bh} = {{E\left\lbrack {{\alpha \; \Delta \; T} - ɛ^{\prime}} \right\rbrack}.}}} & (8)\end{matrix}$

Here α is the difference in the coefficient of thermal expansion betweenthe beam and the substrate, ΔT is the average temperature rise of thebeam, σ_(A) is the axial stress and ε′ is the strain due to beamelongation:

$\begin{matrix}{{ɛ^{\prime} = \frac{l - L}{L}},} & (9)\end{matrix}$

where l is defined as the deformed beam length, which is given by:

$\begin{matrix}{l = {\int_{0}^{L}{\sqrt{1 + \left( \frac{v}{x} \right)^{2}}\ {{x}.}}}} & (10)\end{matrix}$

The assumption of shallow beam curvatures, which can be written asdv/dx<<1, has already been asserted previously in this analysis.Accordingly, the integrand in Eq. (10) can be simplified to:

$\begin{matrix}{{\sqrt{1 + \left( \frac{v}{x} \right)^{2}} \cong {1 + {\frac{1}{2}\left( \frac{v}{x} \right)^{2}}}},} & (11)\end{matrix}$

and the strain term in Eq. (8) can, therefore, be rewritten as:

$\begin{matrix}{ɛ^{\prime} \cong {\frac{1}{2\; L}{\int_{0}^{L}{\left( \frac{v}{x} \right)^{2}\ {{x}.}}}}} & (12)\end{matrix}$

Knowing v(x) from Eq. (3), both the derivative and integral in Eq. (12)can be evaluated. Dropping the approximate equality, combining Eq. (8)and Eq. (12) and rearranging terms gives:

$\begin{matrix}{{\Delta \; T} = {\frac{P}{\alpha \; {Ebh}}{\quad{\left\lbrack {1 + {\frac{3}{4}\left( {e/h} \right)^{2}\begin{Bmatrix}\begin{matrix}{\frac{{\tan \left( {\frac{L}{2}\sqrt{P/{EI}}} \right)}{\cos \left( {2\; L\sqrt{P/{EI}}} \right)}}{L\sqrt{P/{EI}}} +} \\{{\tan^{2}\left( {\frac{L}{2}\sqrt{P/{EI}}} \right)}{\quad{\left\lbrack {1 + \frac{\sin \left( {2\; L\sqrt{P/{EI}}} \right)}{2\; L\sqrt{P/{EI}}}} \right\rbrack +}}}\end{matrix} \\\left\lbrack {1 - \frac{\sin \left( {2\; L\sqrt{P/{EI}}} \right)}{2\; L\sqrt{P/{EI}}}} \right\rbrack\end{Bmatrix}}} \right\rbrack,}}}} & (13)\end{matrix}$

which defines the relationship between applied axial load and averagetemperature rise of the beam.

Nondimensional Design Curves

Collectively, Eq. (4), (7) and (13) fully describe the thermomechanicalbehavior of doubly clamped eccentric beams. For convenience, severalnondimensional parameters can be defined to simplify these equations.Recalling the definition of the critical load, P_(cr), as the force atwhich a theoretically perfect beam (e=0) will buckle:

$\begin{matrix}{{P_{er} = {\frac{\pi^{2}{EI}}{L^{2}} = \frac{\pi^{2}{Ebh}^{3}}{12\; L^{2}}}},} & (14)\end{matrix}$

a Critical Temperature Rise, ΔT_(cr), can be defined by evaluating Eq.(8) at the critical load, noting that for a perfect beam prior tobuckling, there is no deflection and, therefore, no associated strainterm, ε′:

$\begin{matrix}{{\sigma \; T_{er}} = {\frac{P_{er}}{\alpha \; {Ebh}} = {\frac{1}{12\; \alpha}{\left( \frac{\pi \; h}{L} \right)^{2}.}}}} & (15)\end{matrix}$

Utilizing Eq. (14) and (15) and by simple examination of Eq. (4), (7)and (13), nondimensional forms of deflection (δ), eccentricity (ε),axial load (η), maximum compressive stress (Σ) and temperature rise (θ)have been defined respectively as:

$\begin{matrix}{\delta = {d/h}} & {(16)\text{-}(20)} \\{ɛ = {e/h}} & \; \\{\eta = {{\frac{\pi}{2}\sqrt{P/P_{cr}}} = {\frac{L}{2}\sqrt{P/{EI}}}}} & \; \\{\sum{= {\frac{\sigma_{M}}{E}\left( \frac{L}{h} \right)^{2}}}} & \; \\{\theta = {\frac{\Delta \; T}{\Delta \; T_{er}} = {12\; \alpha \; \Delta \; {{T\left( \frac{L}{\pi \; h} \right)}^{2}.}}}} & \;\end{matrix}$

Nondimensional forms of the main relations Eq. (4), (7) and (13) areobtained by rearranging and substituting in Eq. (16)-(20):

$\begin{matrix}{\delta = {ɛ\left\lbrack {{\sec \; \eta} - 1} \right\rbrack}} & (21) \\{\sum{= {\eta^{2}\left\lbrack {\left( {1/3} \right) + {ɛ\; \sec \; \eta}} \right\rbrack}}} & (22) \\{\theta = {{\left( \frac{2\; \eta}{\pi} \right)^{2}\left\lbrack {1 + {\frac{3}{4}ɛ^{2}\left\{ {\frac{\tan \; \eta \; \cos \; 4\eta}{2\eta} + {\tan^{2}{\eta \left( {1 + \frac{\sin \; 4\eta}{4\; \eta}} \right)}} + \left( {1 - \frac{\sin \; 4\eta}{4\eta}} \right)} \right\}}} \right\rbrack}.}} & (23)\end{matrix}$

This set of nondimensional equations was solved numerically usingMATLAB® to eliminate the nondimensional axial load, η. Curves forcentral beam deflection, δ, maximum compressive stress, Σ, and itscorresponding stress components are shown in FIGS. 6-8, respectively, asa functional of temperature rise, θ.

At low temperature rises, θ<<1, the beam behavior is dominated by axialcompression; the beam deflection and stress increase linearly with θ. Athigh temperatures, θ>1, bending begins to be appreciable, leading tolarge deflections and, therefore, large strain. In this range, thestrain term dominates, limiting the beam to finite deflections. Atintermediate temperatures between these two regions, 0.5<θ<1, the shapeof the deflection and stress curves are more sensitive to c and canexhibit very nonlinear behavior as seen in FIG. 6 and FIG. 7.

The curves of deflection as a function of temperature rise shown in FIG.6 pass through an inflection point, denoted here by a circle. This isthe point of maximum slope and the boundary between positive andnegative concavity of the temperature-induced deflection. This makes theinflection point a design parameter of interest for implementing buckledbeams into adaptive structures such as thermally actuated MEMS devices.Accordingly, the location of this point at various eccentricities hasbeen solved numerically utilizing MATLAB®.

First, let δ* and θ* define, respectively, the nondimensional deflectionand temperature rise of the beam at the inflection point. Using thisnotation, the location of the inflection point has been solved andplotted as a function of eccentricity in FIG. 9.

FIGS. 6 and 9 show that for a perfectly symmetric beam, ε=0, there iszero deflection (δ=0) up until buckling occurs at the criticaltemperature, θ≠1. The inflection point is therefore at (δ*, θ*)=(0, 1).For imperfect beams, ε≠0, continuous nonlinear deflections are predictedand the point of maximum slope varies as shown in FIG. 9.

FIGS. 6, 7 and 9 provide succinct nondimensional design curves for theimplementation of thermally actuated buckled beams in MEMS systems.These curves, along with the preceding analysis, capture the complex andhighly nonlinear behavior exhibited in thermally buckled beams. The beamshape, central deflection and state of stress have all been modeled asthey vary with temperature rise and eccentricity.

A beam such as shown in FIGS. 3A and 3B may be fabricated usingsemiconductor fabrication and MEMS fabrication processes as will beappreciated by those of ordinary skill in the art. More specifically, aprocess for fabricating such a beam was described in the provisionalapplication from which the present application claims priority, thedisclosure of which provisional application has been incorporated byreference herein.

Several 300 μm wide beams were fabricated corresponding to two differenteccentricity ratios, e/h, and five different slenderness ratios, L/h.These beams were then measured and compared to the design curvespresented earlier. Table 1 lists all the geometries fabricated for thepresently described example while table 2 lists process conditions fornickel plating the fabricated beams.

TABLE 1 Beam Geometries Beam Length (L) Thickness (h) Eccentricity (e) A1000 μm 30 μm 1.5 μm B 2000 μm 30 μm 1.5 μm C 3000 μm 30 μm 1.5 μm D2000 μm 60 μm 0.75 μm E 3000 μm 60 μm 0.75 μm F 4000 μm+ 60 μm 0.75 μm

Thickness, eccentricity and surface roughness measurements were takenusing a profilometer. The surface roughness was ≦1 μm, while thevariation in thickness across a single beam was measured to be ≦2 μm forthe beams tested in this work.

The nickel electroplating process was optimized to create a depositionwith both low tensile residual stress as well as high yield strength.The plating conditions used in this work, as listed in Table 2, resultedin a deposition rate of approximately 7 μm/hr.

TABLE 2 Process conditions for nickel electroplating with a sulfuractivated anode & mechanical agitation Composition Operating Conditions500 g/L Ni (SO₃NH₂)₂ pH value 4-4.5 30 g/L H₃BO₃ Temperature 35° C. 3g/L Laurel Sulfate Cur. Dens. 10 mA/cm²

Experimental Setup

The beam central deflection, d, was measured experimentally with anoptical probe for the six microfabricated nickel beams listed inTable 1. The beam temperature was controlled using a thin film heaterand a thermocouple. A schematic of the test setup 200 used is shown inFIGS. 10A and 10B which, generally, included an optical probe 202, anickel beam on silicon 204, an aluminum plate 206, a thin film heater208 and a thermocouple 210.

Results and Discussion

The beam central deflection versus temperature rise is plotted againstthe theoretical predictions for all six beams. FIGS. 11A and 11B showgraphs corresponding to the two eccentricity ratios considered in thiswork. Beams A, B and C were electroplated on the same wafer and have aneccentricity ratio of e/h=0.05. Similarly, beams D, E and F werefabricated together and have an eccentricity ratio of e/h=0.0125.

The theoretical results shown here are obtained by evaluating thenondimensional predictions for each beam's specific geometry andadjusting to account for the residual stress. The designed tensileresidual stress in the beams will lead to an actuation temperatureoffset. A small rise in temperature will be required to overcome thetensile stress imparted during microfabrication. The resultanttemperature offsets were used to determine the residual tensile stressin the nickel deposition for the two sets of beams fabricated. Beams A,B and C were offset by a temperature difference of approximately 27° C.,while beams D, E and F were offset by a temperature difference ofapproximately 31° C. The corresponding residual tensile stresses are 54Mpa and 62 Mpa, respectively, for the two sets. These stresses are ingood agreement with the predicted values. A high purity bath of thecomposition and operating conditions used in this work has been reportedto produce depositions with residual tensile stresses of 55 Mpa or less.

Accounting for the temperature offset caused by the residual tensilestress, the ΔT used in the calculation of θ in Eq. (20) can been definedas the temperature rise above the zero stress state, rather than ambientconditions. Accordingly the data for the three beams at a commoneccentricity ratio, ε=e/h, will collapse to a single nondimensionalcurve and can be compared against the predictions.

FIGS. 12A and 12B show relatively good agreement between the theoreticalpredictions and the measured deflections. When presentednondimensionally, the 30 μm beams (A, B and C) show a larger amount ofscatter in the data than that of the 60 μm beams (D, E and F). This isexplained by the sensitivity of the optical probe measurements; thethinner beams have smaller deflections leading to higher percent errors.

It can also be seen that the predictions are less accurate in thetemperature range of 0.5<θ<1. As noted previously, the shape of thedeflection curve in this region is very sensitive to the asymmetry ofthe beam, modeled in this work by the eccentricity ratio ε=e/h. Thiswould suggest that modeling of the beams with a designed imperfection,in the form of an eccentricity, has not completely captured the trueimperfections of the beams tested. Two actual imperfections in thebeams, the surface roughness and the thickness variation, were bothmeasured to be on the order of the designed eccentricities. This seemsto be a logical source of differences between the predictions and testresults in this particular temperature range.

Hysteresis and Yield

The beams tested in the current work were scanned with a profilometerbefore and after thermal actuation to examine the onset and effect ofplastic deformation. The central deflection of the beams after returningback to ambient conditions is listed in Table 3 along with thecalculated maximum stress experienced by each beam.

A nickel electroplating bath of the composition and operating conditionsused in this work has been reported to produce depositions with yieldstrengths of 400 Mpa to 600 Mpa. Table 3 shows the onset of anappreciable hysteresis effect occurring around 450 Mpa for the beamstested in this work.

TABLE 3 Permanent deflection due to plastic deformation and thecorresponding calculated maximum stress for each beam geometry PermanentDeflection Calculated Maximum Stress Beam (μm) (Mpa) A 1.25 400 B 1.00150 C 0.50 75 D 10.25 450 E 4.00 250 F 2.00 150

Repeatability

Two of the low stress beams exhibiting negligible hysteresis effectswere additionally tested to examine the repeatability of the deflectionmeasurements. FIGS. 13A and 13B show good repeatability of the testresults for beams actuated with negligible plastic deformation.

Nomenclature

E modulus of elasticity

l moment of inertia

L pinned-pinned length

M moment

P axial force

ΔT temperature rise

b beam width

d clamped-clamped central deflection

e eccentricity or offset

h beam thickness

deformed beam length

v pinned-pinned lateral deflection

Greek

α difference in CTE of beam and substrate

δ nondimensional deflection, d/h

δ* nondimensional deflection at the inflection point

ε nondimensional eccentricity, e/h

ε′ strain

η nondimensional axial force, ½√{square root over (P/EI)}

θ nondimensional temperature rise, 12αΔT(L/h)²

θ* nondimensional temperature rise at the inflection point

σ compressive stress

Σnondimensional maximum compressive stress,

$\frac{\sigma_{M}}{E}\left( {L/h} \right)^{2}$

Subscripts

A axial

B bending

M maximum

cr critical

While the invention may be susceptible to various modifications andalternative forms, specific embodiments have been shown by way ofexample in the drawings and have been described in detail herein.However, it should be understood that the invention is not intended tobe limited to the particular forms disclosed. For example, while theadaptive structure was described in various embodiments as including abeam, the beam may be configured to exhibit various shapes.Additionally, other configurations besides beams are contemplated. Forexample, a bellows microstructure may be utilized. Thus, the inventionincludes all modifications, equivalents, and alternatives falling withinthe spirit and scope of the invention as defined by the followingappended claims.

1.-26. (canceled)
 27. An adaptive structure comprising: at least onemicrostructure including a microscale beam, the microscale beamcomprising: opposing ends coupled to a surface of a structure; and amiddle portion configured to be displaced relative to the surfaceresponsive to the adaptive structure being exposed to an external heatflux.
 28. The adaptive structure of claim 27, wherein the microscalebeam includes a bimorph structure.
 29. The adaptive structure of claim28, wherein the bimorph structure comprises at least two materialshaving different thermal expansion coefficients.
 30. The adaptivestructure of claim 28, wherein the bimorph structure comprises at leasttwo different metallic materials.
 31. The adaptive structure of claim27, wherein the microscale beam comprises a shape memory alloy.
 32. Theadaptive structure of claim 31, wherein the shape memory alloy comprisestitanium and nickel.
 33. The adaptive structure of claim 32, wherein theshape memory alloy comprises approximately 55% nickel by weight andapproximately 45% titanium by weight.
 34. The adaptive structure ofclaim 27, wherein the middle portion of the microscale beam isconfigured to be displaced away from the surface of the structureresponsive to the adaptive structure being exposed to the external heatflux.
 35. The adaptive structure of claim 27, wherein the surface of thestructure comprises one of a skin panel of a hypersonic vehicle, asurface of a gas turbine component, a surface of a nuclear reactorcomponent, a surface of a combustor component, a surface of a rocketengine component, and a surface positioned for cooling an electroniccomponent.
 36. A structure comprising: a body including a surface; and aplurality of adaptive structures coupled to the surface and configuredto selectively perturb a boundary layer of a fluid adjacent the surfaceof the structure.
 37. The structure of claim 36, wherein the pluralityof adaptive structures comprise flaps.
 38. The structure of claim 36,wherein the plurality of adaptive structures is configured to perturbthe boundary layer of the fluid adjacent to the surface of the structurein response to an external heat flux.
 39. The structure of claim 36,wherein each of the plurality of adaptive structures comprises a shapememory alloy.
 40. The structure of claim 39, wherein the shape memoryalloy comprises titanium and nickel.
 41. The structure of claim 40,wherein the shape memory alloy comprises approximately 55% nickel byweight and approximately 45% titanium by weight.
 42. The structure ofclaim 36, wherein each of the plurality of adaptive structures comprisesa bimorph structure comprising at least two materials having differentthermal expansion coefficients.
 43. The structure of claim 36, whereineach of the plurality of adaptive structures comprises a bimorphstructure comprising at least two different metallic materials.
 44. Thestructure of claim 36, wherein the structure comprises an air foil andthe plurality of adaptive structures is positioned on a surface of theair foil.
 45. A method of thermal management, the method comprising:flowing fluid from a source of fluid to a panel associated with astructure and through a plurality of pores opening onto a surface of thepanel; exposing the panel to an external flow field heat flux; sensinglocal temperatures with a plurality of adaptive structures coupled tothe panel adjacent at least some of the plurality of pores; and alteringa flow of fluid through at least one pore of the plurality of pores withat least one adaptive structure of the plurality of adaptive structures,to vary fluid flow rate through the at least one pore with a thermalload applied by the external flow field heat flux, comprising:displacing a portion of the at least one adaptive structure of theplurality of adaptive structures laterally with respect to an opening ofthe at least one pore.
 46. The method according to claim 45, whereinsensing local temperatures with a plurality of adaptive structurespositioned on a surface of the panel further comprises sensing localtemperatures with a plurality of displacement members of the adaptivestructures.
 47. The method according to claim 44, wherein displacing aportion of the at least one adaptive structure of the plurality ofadaptive structures comprises displacing a portion of at least onedisplacement member of the plurality of displacement members relative tothe at least one pore of the plurality of pores based on the sensedtemperature.
 48. The method according to claim 47, wherein displacingthe portion of the at least one displacement member of the plurality ofdisplacement members comprises displacing a portion of the at least onedisplacement member of the plurality of displacement members thatcomprises a first material and at least a second material, the at leasta second material having a different coefficient of thermal expansionthan the first material.
 49. The method according to claim 47, whereindisplacing the portion of the at least one displacement member of theplurality of displacement members comprises displacing a portion of theat least one displacement member of the plurality of displacementmembers that comprises at least two different metallic materials. 50.The method according to claim 47, wherein displacing the portion of theat least one displacement member of the plurality of displacementmembers comprises displacing a portion of the at least one displacementmember of the plurality of displacement members that comprises a shapememory alloy.
 51. The method according to claim 50, wherein displacingthe portion of the at least one displacement member of the plurality ofdisplacement members comprises displacing a portion of the at least onedisplacement member of the plurality of displacement members thatcomprises a shape memory alloy comprising nickel and titanium.